The present invention is directed to probe shapes for the measurement of time-averaged streamwise momentum and cross-stream turbulence intensity in a turbulent fluid stream and, more particularly, to the measurement of time-averaged streamwise momentum and cross-stream turbulence intensity based on only the streamwise component of the velocity of the fluid stream.
Probes have long been used to measure the total and static pressures in a stream to determine its dynamic pressure, velocity or momentum. Probes indicate the total and static pressures at a specific location in the flow field both simply and without greatly disturbing the surrounding fluid. Since many of the flow fields where these probes are used have low levels of turbulence (i.e., less than 1%), the measurement of total and static pressures is not influenced, to a measurable extent, by the dynamic pressures associated with eddies. However, when measurements are desired in flow fields where the turbulence levels are high, the eddies carry with them significant variations in static and dynamic pressure, and they also generate angles of incidence relative to the probe axis large enough to cause significant errors in the measured quantities. Turbulence levels of such a magnitude occur when the flow field contains energetic shear layers like those found in regions of combustion, along the sides of jets, and in thrust augmenters wherein streams of two different energy levels are mixed and then decelerated. The deceleration lowers the average velocity of the stream without a comparable change in the magnitude and intensity of the eddies. In these kinds of flow fields, the local value of the relative turbulence intensity can exceed 40%. When such a condition is . present, the large variations in local flow direction, static pressure and total head associated with the eddies require that specially designed probe shapes and associated data reduction methods be used to determine the true time-averaged values.
The response of a probe can be quite complex if the probe dimensions are about the same as the eddy sizes, because the flow around the probe is a mixture of several separate flow fields. If, however, the probe is small compared with a typical eddy size, the instantaneous flow field over that part of the probe containing the orifice at which the pressure measurements are made can be approximated by quasi-steady-state theories and experiments. A major source of error arises from the type of response that a given probe shape has to the angle of incidence that is not accounted for in the interpretation of the data. Other factors such as the time-dependent response of the probe flow field to eddy fluctuations and to viscous effects may also contribute to measurement error. The role of the probe shape as having a dominant effect on probe response to angle of incidence is used to develop probe systems that help to determine the properties of highly turbulent streams.
The beginning of the use of pressure probes immersed in a fluid appears to have occurred around 1732 when H. Pitot introduced the idea of placing a probe in a stream to measure the stagnation or impact pressure of water flowing through a duct. Since static pressure was measured at an orifice in the sidewall of the tube, the velocity of the stream could be determined by Bernoulli's equation. Incorporation of these concepts into a single probe embedded in the stream which is capable of making both a total head and a static pressure measurement was introduced by Prandtl (Prandtl et al., Applied Hydro- and Aeromechanics, McGraw-Hill Book Co., Inc., 1934) around 1920. He also made recommendations for the design of the installation so that the effects of the probe and its support on the measurements are minimized. The Prandtl probe functions satisfactorily when its inclination to the flow is small but significant error develops in the measurement of both static and total pressure if the flow angle relative to the probe axis is larger than about 10.degree..
A substantial improvement was made in the acceptance angle of total head probes when G. Kiel (Kiel, "Total Head Meter with Small Sensitivity to Yaw", NACA TM 775, 8/1935) introduced the concept of placing a shroud or shield around the nose of the probe. The shroud increases the capability of the probe to recover the entire stagnation pressure to angles of incidence of 45.degree. or more. Probes of these or related designs are very important in fluid mechanics because of their ability to measure the stream velocity (or the velocity of an aircraft). It is not surprising that a number of studies were undertaken to find more versatile designs and to evaluate the various design parameters in order to minimize measurement errors. One of the earlier papers on the performance of a number of probe configurations was written by Merriam and Spaulding (Merriam et al., "Comparative Tests of Pitot-Static Tubes", NACA TN 546, 11/1935). Subsequent use of these devices and numerous studies of their characteristics are embedded throughout the literature on fluid mechanics.
Extension of steady-state concepts to measurements in unsteady or turbulent flow fields appears to have begun in the early 1930's when it was recognized that turbulence can bring about enough flow angularity, and possibly unsteady-state effects, to influence the magnitude of both total and static pressure measurements. These conjectures were given support by the work of Goldstein (Goldstein, "A Note on the Measurement of Total Head and Static Pressure in a Turbulent Stream", Proceedings of the Royal Society, Series A, Vol. 155, 1936) who derived a correction that is based on the assumption that the time-average of the static pressure and the dynamic pressure is constant along a streamline. He then assumed that the total-head probe being used in the experiment measured the sum of the static pressure and the dynamic pressure associated with the streamwise velocity and with all three components of the turbulence. He did this without making any assumptions regarding the shape of the probe or its response to flow incidence. Without a satisfactory explanation of his theory, Goldstein presented a similar result for the influence of turbulence on measured static pressure. Both of his relationships predict that the effect of turbulence enters the measurement as some factor times the square of the turbulence intensity. Measurements then made by Fage (Fage, "On the Static Pressure in Fully-Developed Turbulent Flow", Proceedings of the Royal Society, Series A, Vol. 155, 1936) in ducts of both circular and rectangular cross-section tended to confirm Goldstein's predictions. Although the results of Goldstein and Fage are open to dispute, they early demonstrated that turbulence in a stream can influence the total and static pressures by an amount that is proportional to the square of the magnitude of the cross-stream turbulence, but they did not make a direct connection with the probe shape and its response to flow incidence caused by the eddies.
Corrsin (Corrsin, "Investigation of Flow in an Axially Symmetrical Heated Jet of Air", NACA ARC No. 3L23, 12/1943) appears to be one of the first to meticulously explore the effect of turbulence on measurements being made in a free jet as it diffuses. The primary objective of his research was to obtain detailed measurements on the structure of free jets and to make comparisons with various theories. Of particular interest in his approach was the use of a mechanism to oscillate hot-wire probes laterally relative to a steady stream so that a calibration could be made of their response to a fluctuating stream. The response curve indicated that the relationship of indicated to actual fluctuations is linear up to about 50% turbulence. As the turbulence increases above 50%, the hot-wire measurement first indicates a value that is slightly larger than the true value. At turbulence levels above about 75%, the value indicated by the hot-wire measurement decreases as the intensity increases.
Investigations were carried out by NACA personnel to develop pressure probes for use in aerodynamic research. A wide variety of configurations was evaluated and guidelines were presented for the installation and use of Pitot/static probes (See Merriam et al. referenced above). One of the objectives of the research was to develop probes that are less sensitive to the angle of incidence in the measurement of stagnation pressure. Some of the configurations studied are illustrated in FIGS. 1a-1g. All of the shapes shown are circular in cross-section. Other cross-sections such as flattened ovals, squares, rectangles, etc. were tested in special situations (e.g., near walls).
The probe for measurement of total pressure with a hemispherical nose shown in FIG. 1a is a simple streamlined shape that is easy to build. Such a shape can be commonly used for a probe that measures both total and static pressure. Another similar shape shown in FIG. 1b has a spherical nose which can be built by drilling a hole through a ball bearing and mounting it on the end of a tube of smaller diameter. An even simpler design shown in FIG. 1c uses a tube that has been cut off so that it is square ended and has no streamlining. The philosophy of such a blunted probe is that the flow over the remainder of the tube is unimportant because measurements are not made downstream of the orifice where the stagnation pressure is measured. The same philosophy applies to the remaining probe shapes presented in FIGS. 1d-1g. A wide variety of internal and external shapes was tried.
The response of probes to flow incidence is of primary interest for making measurements in a turbulent stream. The curves in FIG. 2 present data on how the measured stagnation pressure is affected by angle of incidence. Also shown for comparison is a cosine-squared curve. The probe as shown in FIG. 1d with an internal taper leading to the pressure orifice and duct (where a pressure sensing device is located) has a much greater flow acceptance angle than the hemispherical or spherical nose shapes; that is, it measures the full stagnation pressure to larger flow incidence angles. The shrouded or shielded probes shown in FIG. 1f and expanded upon as shown in FIG. 1g provide an even broader range of incidence angles over which the entire stagnation pressure is recovered with negligible error. Full recovery of stagnation pressure to angles of incidence over 60.degree. has been provided. A probe of this design immersed in a turbulent stream would include in its measurement the full recovery of total pressure of all eddies that induce angles of attack less than about 60.degree.. The contributions of stronger eddies would also be included but not to the full extent.
The flow angularity in a turbulent stream can be measured by use of multiple probes grouped to respond differentially to an unknown flow angle. Other techniques which can be used to interpret measurements made in a turbulent stream include the hot-wire method, laser velocimeter and light-scatter technique.
The relationship between the shape of a probe and its response in a turbulent stream was studied thoroughly by Becker and Brown (Becker et al., "Response of Pitot-Probes in Turbulent Streams", Journal of Fluid Mechanics, Vol. 62, Pt. 1, 1974, pp. 85-114). They determined an equation corresponding to the response of various total-head probe designs to a steady-state flow angle, .alpha.. Two constants, k and m, are used to adapt the equation to various experimentally determined response curves similar to those shown in FIG. 2, ##EQU1## where H.sub.m is the measured stagnation pressure.
U.S. Pat. No.4,836,019 to Hagen et al discloses a compact air data sensor wherein multiple components of a pressure are determined. A probe is constructed with an internally tapered head as shown in FIG. 1d and a circular cross-section. The internally tapered head is merged into the probe's body. The probe can be used to calculate static pressure, impact pressure, angle of attack and angle of sideslip but requires the application of correction factors to do so.
U.S. Pat. No. 3,673,866 to Alperovich et al discloses a pitot tube wherein the tube's measurements are used to determine total head pressure and static pressure. The tube's head section is hemispherical as shown in FIG. 1a and has an orifice which is aligned along the center axis of the tube. A method of compensating for errors in a pressure measurement is shown. The tube, as with standard Pitot tubes, generates significant measurement error if the flow angle relative to the probe axis is substantial.
U.S. Pat. No. 4,718,273 to McCormack discloses a combination alpha, static and total pressure probe wherein a central opening is used to measure total pressure. Several off-axis openings are used to determine angle of attack. Static pressure is measured using several other openings. Data must be interpreted to obtain the desired measurements.